Question

Suppose that the demand and supply functions for good X are

 

 

a.      What are the equilibrium price and quantity?

b.     What is the market outcome if price is $2.75? What do you expect to happen? Why?

c.      What is the market outcome if price is $4.25? What do you expect to happen? Why?

d.     What happens to equilibrium price and quantity if the demand function becomes

e.      What happens to equilibrium price and quantity if the supply function becomes

 (demand is   = 50- 8P)?  

Answer 1

$$solution$$

$Assume\ that: \\ Q_d=50-8P\\ Q_s=-17.5+10P$

A ) The equilibrium is in the point, where $Q_d=Q_s$ So, we put the equations of the demand and supply into the equality.

$50 - 8P = -17.5 + 10P\\ 18P=67.5\\ P=\$3.75 \ is \ the\ equilibrium\ price\\ Q=50-(8\times 3.75)=20\ is\ the\ equilibrium\ quantity$

B] For the lower price the quantity demanded will rise and the quantity supplied will fall, so there will be a shortage of product on the market.

C] For slight increase/ increase in price the quantity demanded will fall and the quantity supplied will rise , so there will be a surplus of the product on the market. 

D] assume the demand function becomes : $Q_d=59-8P?$

Let us repeat the steps from the question {A} above .

$Q_d = Q_s\\ 59 -8P = -17.5 +10P\\ 18P =78.5P\\ P = \$4.36, \\ Q = 59-(8 \times4.36)=24 \ units \ are\ new\ equilibrium \ price\ and \ quantity.$

E] Assume that the supply function be comes:$Qs=-40+10P$

lets repeat the same steps as in {D} above:

$Q_d=Q_S\\ 50-8P=-40+10P\\ 18P=90\\ P=\$5\\ Q=50-(8\times5)=10 \ is \ the \ new \ equilibrium\ price\ and\ quantity.$